# Accelerating optimization-based computed tomography via sparse matrix approximations

## TL;DR

This paper introduces two methods to accelerate computed tomography reconstruction by approximating the Radon transform with sparse matrices, significantly reducing computation time while maintaining reconstruction quality.

## Contribution

It proposes novel sparse matrix approximation techniques for Radon transform evaluations applicable to various iterative algorithms in CT reconstruction.

## Key findings

- Significant reduction in computational time for iterative CT algorithms
- Maintained high-quality reconstructions with the proposed approximations
- Applicable to both general iterative and error-forgetting algorithms

## Abstract

Variational formulations of reconstruction in computed tomography have the notable drawback of requiring repeated evaluations of both the forward Radon transform and either its adjoint or an approximate inverse transform which are relatively expensive. We look at two methods for reducing the effect of this resulting computational bottleneck via approximating the transform evaluation with sparse matrix multiplications. The first method is applicable for general iterative optimization algorithms. The second is applicable in error-forgetting algorithms such as split Bregman. We demonstrate these approximations significantly reduce the needed computational time needed for the iterative algorithms needed to solve the reconstruction problem while still providing good reconstructions.